What is the derivative of f(x)=(e^{3x})/(x^6) ?

The derivative of f(x)=(e^{3x})/(x^6) is (3e^{3x}(x-2))/(x^7)

What is the first derivative of f(x)=(e^{3x})/(x^6) ?

The first derivative of f(x)=(e^{3x})/(x^6) is (3e^{3x}(x-2))/(x^7)

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derivative of

f (x) = \frac{e ^{3 x}}{x ^{6}}

\frac{3 e ^{3 x} ( x - 2 )}{x ^{7}}

Solution steps

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{6}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{3 x} ) x ^{6} - \frac{d}{d x} ( x ^{6} ) e ^{3 x}}{( x ^{6} ) ^{2}}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{e ^{3 x} \cdot 3 x ^{6} - 6 x ^{5} e ^{3 x}}{( x ^{6} ) ^{2}}

Simplify

\frac{e ^{3 x} \cdot 3 x ^{6} - 6 x ^{5} e ^{3 x}}{( x ^{6} ) ^{2}} : \frac{3 e ^{3 x} ( x - 2 )}{x ^{7}}

= \frac{3 e ^{3 x} ( x - 2 )}{x ^{7}}

\frac{d}{d x} (x^{3} + a x^{2} + b x + c)

\frac{d}{d x} (5 x^{2} \cdot ln (x))

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0, y (1) = 4

\int_{0}^{6} (x^{2} - 4) d x

y^{^{'}} + 2 x y = x^{2}

What is the derivative of f(x)=(e^{3x})/(x^6) ?
The derivative of f(x)=(e^{3x})/(x^6) is (3e^{3x}(x-2))/(x^7)
What is the first derivative of f(x)=(e^{3x})/(x^6) ?
The first derivative of f(x)=(e^{3x})/(x^6) is (3e^{3x}(x-2))/(x^7)